Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

Abstract

An analytical set of field-induced coordinates ͑FICs͒ is defined. It is shown that, instead of 3N Ϫ6 normal coordinates, a relatively small number of FICs is sufficient to describe the vibrational polarizability and hyperpolarizabilities due to nuclear relaxation. The fact that the number of FICs does not depend upon the size of the molecule leads to computational advantages. A method is provided for separating anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. Hartree-Fock calculations on a dozen representative conjugated molecules illustrate the procedures and indicate that anharmonicity can be very important. Other potential applications including the determination of zero-point vibrational averaging corrections are noted.

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

“…One obvious choice for monitoring initial convergence is the total order. However, for planar -conjugated oligomers, where anharmonicity plays a major role in determining ␤ (0;0,0), ␥ (0;0,0,0), and ␥ (Ϫ ; ,0,0), it has been found 13 that terms of order I and II are sometimes larger than the zerothorder harmonic terms. It turns out there is another approach to the calculation of pure vibrational hyperpolarizabilities which suggests an alternative grouping of terms that may be more appropriate for determining initial convergence.…”

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

“…That is to say, if (n,m) denotes the order in electrical ͑n͒ and mechanical ͑m͒ anharmonicity, I denotes the sum ͑0,1͒ϩ͑1,0͒ while IIϭ͑0,2͒ϩ͑2,0͒ϩ͑1,1͒. Equations ͑8͒-͑10͒ have also been derived by the property expansion method of Luis et al [28][29][30] For the static ␥ v(r) ͓cf. Eq.…”

“…However, the treatment of small molecules indicates that electrical and mechanical anharmonicity effects can sometimes [23][24][25][26][27][28][29][30][31][32][33] be important and that is the subject of the present paper. In particular, we will examine the second hyperpolarizability of eight different homologous series of conjugated oligomers.…”

Linear response functions for a vibrational configuration interaction state

“…[26][27][28][29] The simplest of these, the so-called double-harmonic ͑DH͒ approximation, 25 which for ␣ is equivalent to the nuclear relaxation contribution to the polarizability ͑␣ nr ͒, 28 considers a harmonic potential and a linear ͑one-mode͒ property surface. Literature values for the PV polarizability of water obtained using these simpler approaches have also been included in Table III. Here we find for ␣ nr that the yy component compares well with the more elaborate results, whereas the zz component is underestimated leading to an overall underestimation of 7.8% for the isotropic polarizability.…”

“…15,16,25 An alternative procedure based on field induced nuclear relaxation geometry optimizations can be used to calculate static or infinite frequency vibrational ͑hyper͒polarizabilities. [26][27][28][29] Variational methods have been more limited in use, and primarily restricted to calculation of zero-point vibrational averages, see for example Ref. 30 and references therein.…”